Graduate-level regression requires more than running a model — it demands understanding assumptions, diagnostics, interpretation, and model selection. I help California graduate students master regression for homework, exams, research, and thesis work.
Regression becomes manageable when you follow a structured modeling workflow: specify the model,
estimate coefficients, check diagnostics, and interpret results with clarity and confidence.
How Tutoring Works
We meet online via Zoom, work through your assignments or datasets, and build a repeatable workflow for regression modeling. You learn by doing — not by watching.
Who This Is For
MS, MBA, MPH, MPP, and PhD students who need help with regression, diagnostics, interpretation, or applied modeling in R, Stata, SPSS, or Python.
Topics Covered in Regression Tutoring
- Simple & Multiple Linear Regression
- Model Assumptions & Diagnostics
- Multicollinearity & Variance Inflation Factors
- Heteroskedasticity & Robust Standard Errors
- Model Selection (AIC, BIC, Stepwise)
- Transformations & Interaction Terms
- Generalized Linear Models (GLM)
- Logistic & Poisson Regression
- Interpreting Coefficients & Marginal Effects
Regression Analysis Concept Explanations (WHY)
Students struggle with regression because it requires understanding both the math behind the model
and the interpretation of results. Multicollinearity, diagnostics, and model selection add layers
of complexity that overwhelm beginners.
Each item below is a one-sentence, exam-ready explanation. Live WHY pages are linked; proposed WHYs are included for academic completeness and future expansion.
Ordinary Least Squares (OLS)
- Why do OLS regression coefficients represent marginal effects holding other variables constant? — OLS isolates partial associations by projecting y onto each regressor net of the others.
- Why do the Gauss-Markov assumptions guarantee OLS is the best linear unbiased estimator? — With exogeneity and homoskedastic errors, OLS has the smallest variance among all linear unbiased estimators.
- Why do t-tests and p-values measure whether a regression coefficient differs from zero? — They compare the estimate to its sampling uncertainty under the null using standardized test statistics.
- Why do we check residual plots when evaluating a regression model? — Residual patterns reveal misspecification (nonlinearity, heteroskedasticity, outliers) that summary stats can hide.
- Why do we use adjusted R² instead of regular R² in multiple regression? — Adjusted R² penalizes unnecessary regressors, reducing the “always increases” bias of plain R².
- Why do we use regression instead of multiple t-tests when analyzing relationships between variables? — Regression models simultaneous controls, reducing omitted-variable confounding and multiple-testing issues.
- Why do we use multiple regression instead of simple regression when analyzing business data? — Business variables move together, so multiple regression isolates partial effects and improves prediction/control.
- Why My Regression Results Don’t Make Sense — When signs/magnitudes look wrong, it’s usually a specification, scaling, multicollinearity, or endogeneity issue rather than “randomness.”
- (proposed) Why does OLS minimize squared residuals? — Squaring penalizes large errors and yields closed-form solutions.
- (proposed) Why do OLS coefficients have a closed-form solution? — The normal equations solve a quadratic optimization problem.
- (proposed) Why does OLS require exogeneity? — If regressors correlate with errors, coefficient estimates become biased.
- (proposed) Why does omitted variable bias occur? — Leaving out a relevant variable that correlates with included regressors distorts coefficients.
- (proposed) Why does R² measure goodness of fit? — It compares explained variance to total variance.
Heteroskedasticity
- Why do we check for heteroskedasticity in regression analysis? — Non-constant error variance breaks standard OLS inference unless corrected with robust methods.
- Why does heteroskedasticity bias standard errors in multiple regression? — Conventional SE formulas assume constant variance, so heteroskedasticity makes them misstate uncertainty.
- (proposed) Why does heteroskedasticity invalidate standard errors? — Unequal error variance violates OLS assumptions and distorts inference.
- (proposed) Why do robust standard errors fix heteroskedasticity? — They adjust the variance estimator without changing coefficients.
- (proposed) Why does weighted least squares help? — It downweights observations with high variance to stabilize estimation.
Multicollinearity
- Why do we check for multicollinearity in multiple regression? — High collinearity inflates coefficient variance, making estimates unstable and tests weak.
- Why does multicollinearity inflate standard errors in multiple regression? — When regressors move together, the model can’t disentangle their separate effects, increasing estimator variance.
- (proposed) Why does multicollinearity inflate standard errors? — Highly correlated regressors make coefficient estimates unstable.
- (proposed) Why does VIF detect multicollinearity? — It measures how much variance is inflated by correlation with other regressors.
- (proposed) Why does centering variables sometimes help? — It reduces non-essential collinearity without changing model fit.
Dummy Variables & Categorical Predictors
- Why do OLS regression coefficients represent marginal effects holding other variables constant? — They isolate partial effects, making dummy variables shift intercepts cleanly.
- (proposed) Why do we omit one category in dummy variable coding? — To avoid perfect multicollinearity (the dummy variable trap).
- (proposed) Why do interaction terms matter? — They allow the effect of one variable to depend on another.
- (proposed) Why do dummy variables shift intercepts? — They represent group-specific baseline differences.
Generalized Linear Models (GLM)
- Why do t-tests and p-values measure whether a regression coefficient differs from zero? — GLMs generalize this logic through likelihood-based inference.
- (proposed) Why do GLMs use link functions? — They connect the linear predictor to the mean of the response distribution.
- (proposed) Why does logistic regression model log-odds? — The logit link maps probabilities to the real line.
- (proposed) Why does maximum likelihood estimation fit GLMs? — It finds parameters that maximize the probability of observed data.
Generalized Method of Moments (GMM)
- Why does endogeneity bias OLS estimates in regression analysis? — GMM solves this by using valid moment conditions that isolate exogenous variation.
- Why does omitted variable bias distort regression coefficients in multiple regression? — GMM can correct this when instruments or valid moments exist.
- Why does omitting a relevant variable bias a regression coefficient upward or downward? — The direction depends on the omitted variable’s effect and correlation with included regressors.
- (proposed) Why does GMM use moment conditions? — They encode population relationships that parameters must satisfy.
- (proposed) Why does GMM generalize IV? — IV is a special case where moments come from instruments.
- (proposed) Why does the weighting matrix affect efficiency? — Optimal weighting minimizes asymptotic variance.
Regression Analysis Troubleshooting (FIX Pages — Proposed)
These issues are fixed by learning a clear modeling workflow, checking diagnostics systematically,
and practicing interpretation with real datasets and structured regression steps.
These FIX pages are planned additions. Each one focuses on spreadsheet or software mechanics — repairing broken calculations, not re-teaching regression concepts.
Excel Regression Models (Proposed)
- Fix Excel OLS regression output — A guide for repairing incorrect ranges, missing labels, and misaligned coefficient tables.
- Fix Excel heteroskedasticity tests — A walkthrough for correcting residual formulas and test-statistic calculations.
- Fix Excel multicollinearity diagnostics — A guide for repairing VIF formulas and correlation matrices.
SPSS, Stata, and R Errors (Proposed)
- Fix SPSS regression “no valid cases” — A guide for identifying missing data, invalid variable types, and empty cells.
- Fix Stata “collinearity detected” — A walkthrough for identifying redundant predictors and dummy-variable traps.
- Fix Stata “no observations” — A guide for resolving dropped categories, filters, and missing values.
- Fix R “object not found” — A walkthrough for correcting environment, naming, and scoping issues.
- Fix R factor vs numeric errors — A guide for converting variable types and avoiding unintended factor behavior.
HOW to Solve Regression Problems
Regression problems are solved by specifying the model, estimating coefficients, checking
diagnostics, and interpreting results in a structured order. Following a consistent modeling
workflow makes complex datasets manageable.
Regression & Linear Models Textbooks
Linear Regression Textbooks
- Kutner, Nachtsheim & Neter — Applied Linear Regression Models
- Fox — Applied Regression Analysis
Generalized Linear Models Textbooks
- Agresti — Foundations of Linear and Generalized Linear Models
Regression Diagnostics Textbooks
- Belsley, Kuh & Welsch — Regression Diagnostics
California Universities Offering Regression & Linear Models Courses
UCLA
- STATS 101A — Regression & Data Analysis
UC Berkeley
- STAT 151A — Linear Modeling
UC Davis
- STA 137 — Applied Time Series
USC
- DSO 510 — Applied Modern Statistical Learning
Stanford
- STATS 216 — Introduction to Statistical Learning
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